Question 1

The receipts for one showing of a movie were $775 for an audience of 150 people. The ticket prices were $7.00 for adults and $4.50 for children under age 12 and adults over age 65. How many adult tickets were sold?
 ________ adult tickets

Accepted Answer

The answer of The receipts for one showing of a...

Question 2

Explain why the following problem does not give enough information to answer the question. The sum of three integers is 48. If the second integer is doubled, the sum is 63. Find the integers.
A) To solve a system of three unknowns, you need two equations. One can only derive one equation from the given information.
B) Doubling the second integer would always result in a sum greater than 63.
C) The parameters given cannot be met -- the equations derived from the first sentence and from the second sentence form an inconsistent system.
D) The parameters given cannot be met by integers -- only rational numbers could be the correct solution to the system of equations derived from this problem.
E) To solve a system of three unknowns, you need three equations. One can only derive two equations from the given information.

Accepted Answer

To solve for three unknowns (the three integers), you need three independent equations. The problem provides two equations: one for the original sum and one for the sum after doubling the second integer. This is insufficient for uniquely determining the three integers.

Question 3

At the ball park, Sarah can buy 5 hotdogs and 7 hamburgers for $57 or 7 hotdogs and 3 hamburgers for $39. What is the price of a hotdog?

Accepted Answer

The answer of At the ball park, Sarah can buy...

Question 4

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Accepted Answer

The answer of Suppose a hammer can be manufactured in...

Question 5

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%?
 $__________ How much was invested at 12%?
 $__________

Accepted Answer

The answer of Part of $9,000 was invested by an...

Question 6

A(n) __________ is a four-sided figure with two pairs of parallel sides.

Accepted Answer

The answer of A(n) __________ is a four-sided figure with...

Question 7

An acute angle is an angle with measure less than 90 degrees. In a right triangle, the measure of one acute angle is 39∘ greater than two times the measure of the other acute angle. Find the measure of each acute angle. __________ $\text { o (smaller) }$  __________ $\text { ° (larger) }$

Accepted Answer

The answer of An acute angle is an angle with...

Question 8

A merchant wishes to mix peanuts that sell for $3 a pound and cashews that sell for $6 a pound to get 70 pounds of mixed nuts that sell for $5 a pound. How many pounds of peanuts should the merchant use?
 ________ pounds of peanuts

Accepted Answer

The answer of A merchant wishes to mix peanuts that...

Question 9

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?
A) 23 expensive, 96 middle-priced, 46 inexpensive
B) 25 expensive, 97 middle-priced, 43 inexpensive
C) 31 expensive, 91 middle-priced, 43 inexpensive
D) 30 expensive, 95 middle-priced, 40 inexpensive
E) 28 expensive, 98 middle-priced, 39 inexpensive

Accepted Answer

The answer of An artist makes three types of ceramic...

Question 10

Find the equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola shown in the illustration.

A) $y = - x ^ { 2 } + 2 x - 4$
B) $y = - x ^ { 2 } - 2 x + 4$
C) $y = x ^ { 2 } - 2 x - 4$
D) $y = x ^ { 2 } + 2 x + 6$
E) $y = x ^ { 2 } + 2 x - 6$

Accepted Answer

The answer of Find the equation of the form \(y...

Question 11

A clothing manufacturer makes coats, shirts, and slacks. The time required for cutting, sewing, and packaging each item is shown in the table. How many of each should be made to use all available labor hours? Coats Shirts Slacks Time available Cutting 20 min 15 min 10 min 120 hr Sewing 60 min 30 min 24 min 310 hr Packaging 5 min 12 min 6 min 58 hr
A) 190 coats, 130 shirts, 160 slacks
B) 190 coats, 140 shirts, 150 slacks
C) 180 coats, 140 shirts, 150 slacks
D) 140 coats, 160 shirts, 150 slacks
E) 150 coats, 140 shirts, 130 slacks

Accepted Answer

The total time available for cutting is 120 hours. The time required for cutting 1 coat is 20 minutes, or 1/3 hour. So, the number of coats that can be cut in 120 hours is 120 / (1/3) = 360 coats.The total time available for sewing is 310 hours. The time required for sewing 1 shirt is 30 minutes, or 1/2 hour. So, the number of shirts that can be sewn in 310 hours is 310 / (1/2) = 620 shirts.The total time available for packaging is 58 hours. The time required for packaging 1 pair of slacks is 6 minutes, or 1/10 hour. So, the number of pairs of slacks that can be packaged in 58 hours is 58 / (1/10) = 580 pairs of slacks.The smallest number of items that can be made is 180 coats, 140 shirts, and 150 slacks.

Question 12

The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is 9 more than the original number. Find the original number.

Accepted Answer

The answer of The sum of the digits of a...

Question 13

How many pounds of each candy shown in the illustration must be mixed to obtain 64 pounds of candy that would be worth $4 per pound?
 
 Gummy Bears: __________ lb Jelly Beans: __________ lb

Accepted Answer

The answer of How many pounds of each candy shown...

Question 14

The owner of a home decorating shop wants to mix dried rose petals selling for $7 per pound, dried lavender selling for $6 per pound, and buckwheat hulls selling for $5 per pound to get 10 pounds of a mixture that would sell for $6.50 per pound. She wants to use twice as many pounds of rose petals as lavender. How many pounds of each should she use?
A) 6 lb of rose petals, 1 lb of lavender, 3 lb of buckwheat hulls
B) 3 lb of rose petals, 6 lb of lavender, 1 lb of buckwheat hulls
C) 1 lb of rose petals, 3 lb of lavender, 8 lb of buckwheat hulls
D) 6 lb of rose petals, 3 lb of lavender, 1 lb of buckwheat hulls
E) 1 lb of rose petals, 8 lb of lavender, 3 lb of buckwheat hulls

Accepted Answer

Let the number of pounds of lavender be x. Then, the number of pounds of rose petals must be 2x. The total mixture is 10 pounds, so the number of pounds of buckwheat hulls is 10 - x - 2x = 10 - 3x.

Now, we can set up the equation:

(7)(2x) + (6)(x) + (5)(10 - 3x) = (6.5)(10)

14x + 6x + 50 - 15x = 65

5x = 1

x = 0.2

So the number of pounds of lavender needed is x = 0.2, which means the number of pounds of rose petals needed is 2x = 0.4. The number of pounds of buckwheat hulls needed is 10 - x - 2x = 9.4.

Therefore, the answer is D: 6 lb of rose petals, 3 lb of lavender, 1 lb of buckwheat hulls.

Question 15

The jet stream is a wind current that flows across the United States from west to east. Flying with the jet stream, an airplance flew 3,500 miles in 5 hours. Against the same wind, the return trip took 7 hours. Find the speed of the plane in still air and the speed of the jet stream. ________ mph speed of plane in still air ________ mph speed of jet stream

Accepted Answer

The answer of The jet stream is a wind current...

Question 16

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same?
 ______ minutes

Accepted Answer

The answer of A long distance provider offers two plans....

Question 17

Comets have elliptical orbits, but the orbits of some comets are so vast that they are indistinguishable from parabolas. Find an equation of the form $y = a x ^ { 2 } + b x + c$ for the parabola that closely describes the orbit of the comet shown in the illustration.

A) $y = - \frac { 1 } { 2 } x ^ { 2 } - x - \frac { 9 } { 2 }$
B) $y = \frac { 1 } { 2 } x ^ { 2 } - x - \frac { 9 } { 2 }$
C) $y = - \frac { 1 } { 2 } x ^ { 2 } - x + \frac { 9 } { 2 }$
D) $y = \frac { 1 } { 2 } x ^ { 2 } + x - \frac { 9 } { 2 }$
E) $y = \frac { 1 } { 2 } x ^ { 2 } + x + \frac { 9 } { 2 }$

Accepted Answer

The parabolic orbit appears to open downwards and have a vertex below the origin. Therefore, options A and C can be eliminated. Looking at the shape of the orbit, it appears to be wider than it is tall, so the coefficient of x squared should be positive. Therefore, options D and E can be eliminated. Plugging in some of the points on the orbit, we can check which option matches the most points. Using option B, we get that the orbit passes through the points (-3, 0), (0, -9), and (3, 0), which closely matches the orbit shown in the illustration. Therefore, the answer is B.

Question 18

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.
A) $v ^ { - 3 }$
B) $( - 2 , - 12 )$
C) $9 x ^ { 2 } - 24 x + 15$
D) $3 x ^ { 2 } - 3$
E) $x = 4$

Accepted Answer

The answer of The sum of the angles in any...

Question 19

The sum of the digits of a two-digit number is 9. If the digits are reversed the new number is 9 less than the original number. Find the original number.

Accepted Answer

The answer of The sum of the digits of a...

Question 20

A piece of cheese toast has 111 calories. The bread has fifteen more calories than the cheese. Find the number of calories in the bread. ________ calories in bread

Accepted Answer

The answer of A piece of cheese toast has 111...

Quiz 3: Systems of Equations

The receipts for one showing of a movie were $775 for an audience of 150 people. The ticket prices were $7.00 for adults and $4.50 for children under age 12 and adults over age 65. How many adult tickets were sold? ________ adult tickets

Explain why the following problem does not give enough information to answer the question. The sum of three integers is 48. If the second integer is doubled, the sum is 63. Find the integers.

At the ball park, Sarah can buy 5 hotdogs and 7 hamburgers for $57 or 7 hotdogs and 3 hamburgers for $39. What is the price of a hotdog?

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $ How much was invested at 12%? $

A(n) __________ is a four-sided figure with two pairs of parallel sides.

An acute angle is an angle with measure less than 90 degrees. In a right triangle, the measure of one acute angle is 39∘ greater than two times the measure of the other acute angle. Find the measure of each acute angle. $\text { o (smaller) }$ $\text { ° (larger) }$

A merchant wishes to mix peanuts that sell for $3 a pound and cashews that sell for $6 a pound to get 70 pounds of mixed nuts that sell for $5 a pound. How many pounds of peanuts should the merchant use? ________ pounds of peanuts

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?

The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is 9 more than the original number. Find the original number.

How many pounds of each candy shown in the illustration must be mixed to obtain 64 pounds of candy that would be worth $4 per pound? Gummy Bears: lb Jelly Beans: lb

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same? ______ minutes

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.

The sum of the digits of a two-digit number is 9. If the digits are reversed the new number is 9 less than the original number. Find the original number.

A piece of cheese toast has 111 calories. The bread has fifteen more calories than the cheese. Find the number of calories in the bread. ________ calories in bread

Quiz 3: Systems of Equations

The receipts for one showing of a movie were $775 for an audience of 150 people. The ticket prices were $7.00 for adults and $4.50 for children under age 12 and adults over age 65. How many adult tickets were sold? ________ adult tickets

Explain why the following problem does not give enough information to answer the question. The sum of three integers is 48. If the second integer is doubled, the sum is 63. Find the integers.

At the ball park, Sarah can buy 5 hotdogs and 7 hamburgers for $57 or 7 hotdogs and 3 hamburgers for $39. What is the price of a hotdog?

Suppose a hammer can be manufactured in two different ways. The number of hammers that will cost equal amounts to produce either way is called the ________ point.

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $__________ How much was invested at 12%? $__________

A(n) __________ is a four-sided figure with two pairs of parallel sides.

A merchant wishes to mix peanuts that sell for $3 a pound and cashews that sell for $6 a pound to get 70 pounds of mixed nuts that sell for $5 a pound. How many pounds of peanuts should the merchant use? ________ pounds of peanuts

An artist makes three types of ceramic statues at a monthly cost of $650 for 165 statues. The manufacturing costs for the three types are $5, $4, and $3. If the statues sell for $20, $12, and $9, respectively, how many of each type should be made to produce $2,100 in monthly revenue?

Find the equation of the form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c for the parabola shown in the illustration.

The sum of the digits of a two-digit number is 15. If the digits are reversed the new number is 9 more than the original number. Find the original number.

How many pounds of each candy shown in the illustration must be mixed to obtain 64 pounds of candy that would be worth $4 per pound? Gummy Bears: __________ lb Jelly Beans: __________ lb

A long distance provider offers two plans. Plan 1 has a monthly fee of $10 plus $0.14 per minute. Plan 2 has a monthly fee of $16 plus $0.12 per minute. For what number of minutes will the cost of the plans be the same? ______ minutes

Comets have elliptical orbits, but the orbits of some comets are so vast that they are indistinguishable from parabolas. Find an equation of the form y=ax2+bx+cy = a x ^ { 2 } + b x + cy=ax2+bx+c for the parabola that closely describes the orbit of the comet shown in the illustration.

The sum of the angles in any triangle is 5x=95 ^ { x } = 95x=9 . In triangle ABC , angle A is −0.5579- 0.5579−0.5579 less than the sum of angles B and C , and angle C is −1.7925- 1.7925−1.7925 less than twice angle B . Find each angle.

The sum of the digits of a two-digit number is 9. If the digits are reversed the new number is 9 less than the original number. Find the original number.

A piece of cheese toast has 111 calories. The bread has fifteen more calories than the cheese. Find the number of calories in the bread. ________ calories in bread

Part of $9,000 was invested by an investment club at 10% interest and the rest at 12%. The annual income from these investments is $1,060. How much was invested at 10%? $ How much was invested at 12%? $

How many pounds of each candy shown in the illustration must be mixed to obtain 64 pounds of candy that would be worth $4 per pound? Gummy Bears: lb Jelly Beans: lb

The sum of the angles in any triangle is $5 ^ { x } = 9$ . In triangle ABC , angle A is $- 0.5579$ less than the sum of angles B and C , and angle C is $- 1.7925$ less than twice angle B . Find each angle.